ERIC NOTEBOOK SERIES

Second Edition

Risk and Rate Measures in Cohort Studies

Second Edition Authors: Cohort studies are longitudinal developing the outcome of interest). studies where an exposed and an Person-time can be measured in days, Lorraine K. Alexander, DrPH unexposed group (or less exposed months, or years, depending on the group) are followed forward in time unit of time that is relevant to the Brettania Lopes, MPH to find the incidence of the outcome study. A rate measures the rapidity of Kristen Ricchetti-Masterson, MSPH of interest (e.g. disease, death, or health outcome occurrence in the change in health). Two measures of population. Karin B. Yeatts, PhD, MS incidence are risks and rates. Risks and rates can be further manipulated to provide

additional information on the effects Two-by-two tables are generally used of the exposure of interest, such as to organize the data from a study as risk ratios, rate ratios, attributable shown below. risks (risk or rate differences) Disease No disease Total and attributable risk percent. Exposed a b a+b Risk is defined as the Unex- c d c+d number of new cases divided posed by the total population-at-risk Total a+c b+d a+b+c+d at the beginning of the follow- up period. An individual's risk of Risk ratios. developing the outcome of interest is When risks are computed in a study, the risk ratio is the measure that

compares the Riskexposed to the Risk . The risk ratio is defined measured. unexposed as the risk in the exposed cohort (the A rate is the number of new cases of index group) divided by the risk in the a health outcome divided by the unexposed cohort (the reference total person-time-at-risk for the group). A risk ratio may vary from zero to infinity. population. Person-time is calculated Risk Ratio = [a / (a+b)] / [c by the sum total of time all individuals remain in the study without developing the outcome of interest (the total amount of time

that the study members are at risk of

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ERIC NOTEBOOK PA G E 2

For example, suppose researchers conduct a cohort study person- years, or 0.34 cases/person-year. The rate in the and gather the following data on the effects of gasoline unexposed cohort is 25/188 person-years, or 0.13 cases/ fume exposure on respiratory illness among automotive person-year. The rate ratio in this study is 0.34/0.13, or workers. 2.6, which is higher than the rate ratio calculated above. This rate ratio reveals that respiratory illness among Disease No disease Total workers exposed to gasoline fumes is developing at 2.6 Exposed 60 140 200 times the rate that respiratory illness is developing among workers not exposed to gasoline fumes. Unex- 25 175 200

posed An exposure may be preventive (e.g., vitamin intake) or Total 85 315 400 harmful (e.g., toxic chemical exposure). Confounding, which you will read about in another ERIC notebook issue, In this study, the risk in the exposed group is 60/200, or is one type of systematic error that can occur in 0.30 cases per person (30 cases per 100 people), and the epidemiologic studies. Confounding can cause an over- or risk in the unexposed group is 25/200, or 0.125 cases per under-estimate of the observed association between person (13 cases per 100 people). Therefore, the risk ratio exposure and a health outcome. Assuming there are no is 0.30/0.125, or 2.4. A risk ratio of 2.4 implies that the other factors that may confound the association, a risk exposed group has 2.4 times the risk of developing ratio less than 1 indicates that the risk in the exposed respiratory illness as the unexposed group. (index) group is less than the risk in the unexposed or less -exposed (reference) group, and therefore, the exposure is Rate ratio preventive. A risk ratio or rate ratio that equals 1 (the null value) indicates that there is no difference in risk or rates When rates are computed in a study, the rate is the between exposed and unexposed groups. A risk ratio measure that compares the Rateexposed to Rateunexposed . greater than one indicates that the risk in the exposed is The rate ratio is defined as rate of health outcome occurrence in the exposed cohort index group) divided greater than the risk in the unexposed, and, therefore, the by the rate of occurrence in the unexposed exposure is harmful. or less-exposed cohort (the The following table may be applied to both risk and rate ratios.

The farther away the risk ratio or rate ratio is from the null Disease No disease Person-years at value of one, the greater the effect of exposure is on the risk study group. This is shown in the following diagram. Exposed 60 140 175 Unexposed 25 175 188

Total 85 315 363

In this study, the rate in the exposed cohort is 60/175 RR=risk ratio or rate

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ERIC NOTEBOOK PA G E 3

Rate differences Practice Questions

In order to find the absolute effect of an exposure a health Answers are at the end of this notebook outcome the attributable rate (AR), or rate difference, must be computed. The term attributable rate is same as 1) Researchers conduct a prospective cohort study to rate difference (RD). The attributable rate is the excess assess the association between dietary supplements and rate among the exposed population attributed to exposure. cognitive ability among children. A total of 500 children It is defined as the rate in the exposed minus the rate in the unexposed. The rate difference can also be reported age 12-17 years who take an omega-3 fatty acid as a percent (see figure below). supplement are compared with 500 children age 12-17 years who do not take an omega-3 fatty acid supplement. Researchers follow the children for 2 years. During this time, 300 children who take the supplement earn what is classified as a “high” score on a cognitive test while 200 children who do not take the supplement earn what is classified as a “high” score on the same cognitive test.

a) Construct a 2x2 table from the information presented above

b) The risk attributable to exposure is:

c) The attributable risk percent in the total population is:

d) The risk difference among the exposed is:

2) Researchers conduct a prospective cohort study of the RD%(exposed)= risk in exposed – risk in unexposed x 100 association between working at a high-stress job and risk in exposed depression. A total of 5000 adults are followed for an average of 10 years. Among these 5000 adults, 2500 had a high-stress job while 2500 had a low-stress job. RD%(total population)= risk in total pop– risk in unexposed x 100 risk in total population Participants had yearly health checks. A total of 250 incident cases of depression were diagnosed in the high- stress job group while 90 incident cases of depression Rate Difference = Rateexposed - Rateunexposed were diagnosed in the low-stress job group. Assume all cases of depression were diagnosed at the end of year 5 of follow-up.

a) Construct a 2x2 table from the information above

b) Rate exposed =

Rate unexposed =

c) Rate ratio = d) Rate difference=

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ERIC NOTEBOOK PA G E 4

References Answers to Practice Questions Dr. Carl M. Shy, Epidemiology 160/600 Introduction to 1. Epidemiology for Public Health course lectures, 1994- a) 2001, The University of North Carolina at Chapel Hill, Scored “high” Did not score Total Department of Epidemiology on exam “high” on ex- am Rothman KJ, Greenland S. Modern Epidemiology. Second Exposed to 300 200 500 Edition. Philadelphia: Lippincott Williams and Wilkins, supplement Unexposed 200 300 500 1998. to supple- ment The University of North Carolina at Chapel Hill, Department Total 500 500 1000 of Epidemiology Courses: Epidemiology 710,

Fundamentals of Epidemiology course lectures, 2009- b) Risk exposed = 300/500= 0.6 cases/person 2013, and Epidemiology 718, Epidemiologic Analysis of Risk unexposed = 200/500 = 0.4 cases/person Binary Data course lectures, 2009-2013. c) Risk total population = 500/1000 = 0.5 cases/person

d) Risk difference = 0.6 – 0.4 = 0.2 cases/person Acknowledgement The authors of the Second Edition of the ERIC Notebook 2. would like to acknowledge the authors of the a) ERIC Notebook, First Edition: Michel Ibrahim, Study Depres- No de- Total person- MD, PhD, Lorraine Alexander, DrPH, Carl Shy, group sion pression years MD, DrPH, and Sherry Farr, GRA, Department of High- 250 2250 (250*5+2250*10) stress = 23,750 Epidemiology at the University of North Carolina job at Chapel Hill. The First Edition of the ERIC Low- 90 2410 (90*5+2410*10)= Notebook was produced by the Educational Arm stress 24,550 of the Epidemiologic Research and Information job Center at Durham, NC. The funding for the ERIC Total 340 4660 48, 300 Notebook First Edition was provided by the Department of Veterans Affairs (DVA), Veterans Health Administration (VHA), Cooperative b) Rate exposed = 250/23,750 person years * 10,000 = Studies Program (CSP) to promote the strategic 105.3 cases/ 10,000 person years growth of the epidemiologic capacity of the DVA. Rate unexposed = 90/24,550 person years * 10,000 =

36.7 cases/ 10,000 person years

c) Rate ratio = 105.3 cases/ 10,000 person years / 36.7

cases/ 10,000 person years = 2.87

d) Rate difference = 105.3 cases/ 10,000 person years - 36.7 cases/ 10,000 person years = 68.6 cases/10,000 person-years

ERIC at the UNC CH Department of Epidemiology Medical Center